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On the Number of Nodal Domains of Toral Eigenfunctions

Research output: Contribution to journalArticlepeer-review

Original languageEnglish
Article number17
Pages (from-to)3027–3062
JournalAnnales Henri Poincare
Volume2016
Early online date28 Mar 2016
DOIs
Accepted/In press2 Feb 2016
E-pub ahead of print28 Mar 2016
PublishedNov 2016

King's Authors

Abstract

We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov–Sodin’s results for random fields and Bourgain’s de-randomisation procedure we establish a precise asymptotic result for “generic” eigenfunctions. Our main results in particular imply an optimal lower bound for the number of nodal domains of generic toral eigenfunctions.

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